Question

Dada uma progressão geométrica infinita, sabemos que a razão é 1/3 e que a soma dos termos dessa progressão vale 54. Podemos afirmar que o primeiro termo dessa progressão é o: *
(a)16
(b)26
(c)36
(d)46
(e)56​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf Soma\,dos\,termos\,de\,uma\,PG\,infinita.}\\\huge\boxed{\boxed{\boxed{\boxed{\rm S_n=\dfrac{a_1}{1-q}}}}}\end{array}}$

$\large\boxed{\begin{array}{l}\sf dados\begin{cases}\rm q=\dfrac{1}{3}\\\\\rm S_n=54\\\rm a_1=?\end{cases}\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm S_n=\dfrac{a_1}{1-q}\longrightarrow a_1=S_n\cdot(1-q)\\\\\rm a_1=54\cdot\bigg(1-\dfrac{1}{3}\bigg)\\\\\rm a_1=\diagup\!\!\!\!\!54\cdot\bigg(\dfrac{2}{\backslash\!\!\!3}\bigg)\\\\\rm a_1=18\cdot2\\\rm a_1=36\\\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger\red{\maltese}~\blue{alternativa~c}}}}}\end{array}}$